Exact count verification
========================
Range: k=0,...,10000, corresponding to even total sizes N=0,...,20000.
Number of reconstructed values: 10001.
The exact run used 17 prime moduli with a 527-bit CRT product.
p(20000) has 507 bits.
Since 0 <= a_N <= p(N), the CRT reconstruction is unique.
The original run checked every reconstructed value modulo the independent prime 2147483171.
The packaged values for k=0,...,750 agree with the preceding public OEIS b-file snapshot.
a_20000 = 536431000755049008083017324089784667126327625235073409851254086081372896267600672905174354106135651274303522996555223053595523405467923436009629038154
a_20000 / p(20000) = 2.127725033856734269214780E-3
